Raisman followed up on her bronze on the beam with an impressive performance to score 15.600 and claim the title ahead of Romania's Catalina Ponor in silver (15.200).
Russian Aliya Mustafina took bronze with a score of 14.900.
Defending Olympic champion Sandra Raluca Izbasa of Romania, the last gymnast to compete, missed out after a fall on her last tumbling combination to finish bottom of the field.
'Today has been a dream come true,' Raisman said.
'I'm so glad I got the medal I wanted. It was the best routine I've ever done. My coach said it was the best routine he'd ever seen me do.
'To have won a gold medal, two gold medals (one in the team final), is really special.'